Question

Find the derivative of the function using the definition of derivative. f(x) = 1 / (x^2 - 36) f'(x) = State the domain of the function. (Enter your answer using interval notation.) (-?, ?) State the domain of its derivative. (Enter your answer using interval notation.) [-?, 0)

          Find the derivative of the function using the definition of derivative.
f(x) = 1 / (x^2 - 36)
f'(x) =
State the domain of the function. (Enter your answer using interval notation.)
(-?, ?)
State the domain of its derivative. (Enter your answer using interval notation.)
[-?, 0)

Find the derivative of the function using the definition of derivative.
f(x) = 1 / (x^2 - 36)
f'(x) =
State the domain of the function. (Enter your answer using interval notation.)
(-?, ?)
State the domain of its derivative. (Enter your answer using interval notation.)
[-?, 0)

Added by Remedios C.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Steven Clarke

02/01/2022

Step 1

Given function: \( f(x) = x^2 - 36 \) Using the definition of derivative, we have: \[ f'(x) = \lim_{{h \to 0}} \frac{f(x + h) - f(x)}{h} \] \[ f'(x) = \lim_{{h \to 0}} \frac{(x + h)^2 - 36 - (x^2 - 36)}{h} \] \[ f'(x) = \lim_{{h \to 0}} \frac{x^2 + 2xh + h^2 - 36 Show more…

Show all steps

Thanks for your feedback!

Find the derivative of the function using the definition of derivative. f(x) = 1 / (x^2 - 36) f'(x) = State the domain of the function. (Enter your answer using interval notation.) (-∞, ∞) State the domain of its derivative. (Enter your answer using interval notation.) [-∞, 0)